Import Question JSON

Current Question (ID: 8717)

Question:

$\text{If } u_1 \text{ and } u_2 \text{ are the units selected in two systems of measurement and } n_1 \text{ and } n_2 \text{ are their numerical values, then:}$

Options:

1. $n_1u_1 = n_2u_2$
2. $n_1u_1 + n_2u_2 = 0$
3. $n_1n_2 = u_1u_2$
4. $(n_1 + u_1) = (n_2 + u_2)$

Solution:

\text{Explanation:} \text{The fundamental principle of unit conversion states that a physical quantity remains constant regardless of the unit system used to measure it.} \text{If the same physical quantity is measured in two different systems:} \text{Physical quantity} = n_1 \times u_1 = n_2 \times u_2 \text{Therefore: } n_1u_1 = n_2u_2 \text{Example: If a length is 100 cm in one system and 1 m in another system:} n_1 = 100, \quad u_1 = \text{cm}, \quad n_2 = 1, \quad u_2 = \text{m} \text{We verify: } 100 \times \text{cm} = 1 \times \text{m} = 100 \text{ cm} \text{Options 2, 3, and 4 are dimensionally incorrect or physically meaningless.}

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}